Polynomials and their Potential Theory for Gaussian Radial Basis Function Interpolation
Date
2004
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Department of Mathematical Sciences
Abstract
We explore a connection between Gaussian radial basis functions and polynomials. Using standard tools of potential theory, we find that these radial functions are susceptible to the Runge phenomenon, not only in the limit of increasingly flat functions, but also in the finite shape parameter case. We show that there exist interpolation node distributions that prevent such phenomena and allow stable approximations. Using polynomials also provides an explicit interpolation formula that avoids the difficulties of inverting interpolation matrices, without imposing restrictions on the shape parameter or number of points.
Description
Keywords
Gaussian radial basis functions, RBF, potential theory, Runge phenomenon, convergence, stability